It's genetics, hon. Tweezers are your friend, if you want to make a change in how they look. Or you can rock it like Brooke Shields does.
Is it normal for a girl to have thick eyebrows?
It depends on your facial features. If you are crazy hairy then of course your going to want to trim back the brows a bit. If you have small eyes your also going to want to trim the brows so they don't over power your eyes. But as long as thats not the case then thicker eyebrows that are controlled with propper trimming and waxing can be very beautiful.